A general discrete method approach for particulate materials

Computational approaches of mechanical systems based on the continuum hypothesis, are sometimes inaccurate and not reliable. As an example, problems involving severe mesh distortion, geometric discontinuities or characterized by an assembly of discrete parts, are not easily solvable within the Lagrangian continuum framework, such as by using the classical finite element method. Computational approaches based on the description of the domain without the need of a mesh connectivity, would be useful to overcome this drawbacks. On the other hand a discrete approach is a particularly suitable tool for modeling materials at the microscale where its particulate nature becomes evident. The Lagrangian-based meshless formulation—known as smoothed particle hydrodynamics (SPH)—has been widely applied to different engineering fields. In the present research a general force potential-based particle method falling within the SPH framework for the mechanical simulation of granular and continuum materials under dynamic condition, is developed. The particle–particle and particle-boundary interaction is modeled through force functionals, tuned according to the nature of the material being analyzed (solid, granular, …). The proposed potential-based formulation allows the description of the forces existing between the discrete elements of generic materials. Thanks to the capability to deal with short and long distance actions (namely mechanical and/or electrostatic), general force–deformation laws, etc. it allows a straightforward mechanical simulation of fine particles assemblies such as powders. The theoretical basis of the computational approach are presented and some examples involving powder motion and a continuum mechanical problem are illustrated and discussed.